Here is a quick look at a full frame vs crop sensor comparison using a camera such as the 5d mk3 and an APS-C or crop sensor camera such as the 60D.
In this video we get an idea of what to expect when you compare the field of view (what’s in the frame) and depth of field (range of the area in focus) using a 50mm prime lens on both cameras.
I primarily shoot video with crop sensor cameras and tend to forget the aesthetic and “look” full frame cameras can give you.
Generally speaking for video, full frame cameras perform better in low light but crop sensor cameras are cheaper to purchase.
Regardless of which tool you have or are looking to use for your video production both have the ability to look great.